Harry's wards and threshold ?
The wards: I've been looking, and I can't find anything to say whether or not Harry's wards would affect someone coming into his home from the Nevernever. If they're set up around the physical structure of the building, they may not. Harry once said that he had wards around the door and windows, but even if they completely surrounded his apartment, they might not cover entrance from the spirit world. Prior to
Changes, we've never seen any travel from one side to the other while in Harry's house, so there hasn't been much commentary to go on.
The threshold: A threshold wouldn't stop Mab. Even if it killed 99% of her power, she would probably still have more than enough left to stomp Harry into the dirt, which would be more than enough to fix Little Chicago. And Harry's threshold has never been stellar to begin with. It would not be an impediment to her if she chose to enter his lab.